Approximate Value - Logarithm

Category: Differential Calculus, Algebra

"Published in Suisun City, California, USA"

Find the approximate value of log 97 without using a calculator or logarithm table.

Solution:

We know that the log 100 is 2. How do you get a logarithm of a number without using a calculator or logarithm table? Is that possible? Yes, we can get the approximate value of logarithm of any number (except ≤ 0) as follows

Let

then

If   x = 100
   dx = 97 - 100 = -3
     e = 2.7182818284590452353602874713527....

then dy will be

Therefore

using a calculator

from logarithm table